text: There are several limits that can be analyzed to make the study of resonance fluorescence easier. The first of these is the approximations associated with the Weak Field Limit, where the square modulus of the Rabi frequency of the field that is coupled to two-level atom is much smaller than the rate of spontaneous emission of the atom. This means that the difference in the population between the excited state of the atom and the ground state of the atom is approximately independent of time. 
  If we also take the limit in which the time period is much larger than the time for spontaneous decay, the coherences of the light can be modeled as 
  , where  is the Rabi frequency of the driving field and  is the spontaneous decay rate of the atom. Thus it is clear that when an electric field is applied to the atom, the dipole of the atom oscillates according to driving frequency and not the natural frequency of the atom. If we also look at the positive frequency component of the electric field, 
  we can see that the emitted field is the same as the absorbed field other than the difference in direction, resulting in the spectrum of the emitted field being the same as that of the absorbed field. The result is that the two-level atom behaves exactly as a driven oscillator and continues scattering photons so long as the driving field remains coupled to the atom.
  The weak field approximation is also used in approaching two-time correlation functions. In the weak-field limit, the correlation function  can be calculated much more easily as only the first three terms must be kept. Thus the correlation function becomes 
   as .
  From the above equation we can see that as  the correlation function will no longer depend on time, but rather that it will depend on . The system will eventually reach a quasi-stationary state as 
  It is also clear that there are terms in the equation that go to zero as . These are the result of the Markovian processes of the quantum fluctuations of the system.
  We see that in the weak field approximation as well as , the coupled system will reach a quasi-steady state where the quantum fluctuations become negligible.